The invention is based on an apparatus and method of making an apparatus for measuring the mass of a flowing medium. In apparatus of this kind, that is, in so-called hot films, it is necessary for the temperature-dependent resistor layer or film to have a predetermined resistance value. In particular in the case of resistor films connected in series and disposed on both sides of the carrier, the resistance values must be as nearly identical as possible and must react with equal speed to changes in the flow speed of the medium.